Sometimes. Carpal tunnel happens in individuals who are predisposed to having excessive pressure on their median nerves at the wrist by virtue of their wrist anatomy i.E smaller or larger carpal tunnel, sensitive nerve. On top of that predisposition, overuse of the wrist and specifically flexing/extension will bring on symptoms. While work can certainly contribute so can any other use if the hand and wrist.
Possibly. Cts can also result from trauma to the wrist (fall, crush injury). Not all state work comp rules recognize cts as a work related issue, particularly, if it is attributed to "overuse, " such as typing, keyboard, etc. Generally, if there is a chance that it might be accepted, you can expect a thorough investigation in to your life, to make sure that there is no other possible cause.
POssibly. It is tough to establish causality in many situations but htere are cases where it is felt to be work related at times.